On SU(2) Wess-Zumino-Witten models and stochastic evolutions

It is discussed how stochastic evolutions may be connected to SU(2) Wess-Zumino-Witten models. Transformations of primary fields are generated by the Virasoro group and an affine extension of the Lie group SU(2). The transformations may be treated and linked separately to stochastic evolutions. A combination allows one to associate a set of stochastic evolutions to the affine Sugawara construction. The singular-vector decoupling generating the Knizhnik-Zamolodchikov equations may thus be related to stochastic evolutions. The latter are based on an infinite-dimensional Brownian motion.